Piezoelectric accelerometers of various designs have been used for decades in connection with structureborne and fluidborne sound measurements. A broad set of applications where they have been used include vibration monitoring of machinery, shock evaluation of structures, seismic sensing, and underwater acoustic surveillance. When low frequency applications are considered (e.g., frequencies below 10 kHz) flexural mode accelerometers are often used because they have excellent performance characteristics and can be fabricated in a reasonably straightforward manner. High frequency applications are better served with compression and shear mode accelerometers because the resonance frequency of such devices is typically in the ultrasonic range and therefore facilitates a flat receiving sensitivity over a relatively large bandwidth. For a general discussion on the basic operating principles of accelerometers, refer to G. Gautschi, Piezoelectric Sensorics: Force, Strain, Pressure, Acceleration, and Acoustic Emission Sensors, Materials and Amplifiers (Springer, Berlin, 2006) pp. 167-197, incorporated by reference herein.
Historically speaking, the most pervasive flexural mode accelerometer design is the so-called trilaminar piezoelectric cantilever beam in which a sensing structure comprised of a fixed-free metal beam outfitted with a pair of piezoelectric plates is used to convert dynamic motion to an output voltage that can be processed and displayed to glean useful information about a measurement. Depending on the design, a proof-mass may optionally be included at the free end of the beam so that the operational bandwidth and sensitivity are tuned to specific values. Examples of devices that utilize cantilever beam accelerometers include those described in U.S. Pat. Nos. 2,722,614, 4,333,029, and 4,709,359, each incorporated by reference herein. In all cases it is important to note that the piezoelectric plates associated with these devices comprise a polycrystalline ceramic composition such as lead zirconate titanate (PZT) and a single composite cantilever beam is utilized.
In the late 1990s, researchers discovered that relaxor-based piezoelectric single crystal materials had superior elasto-piezo-dielectric properties relative to those of polycrystalline ceramics. These improved properties naturally led to devices exhibiting higher figure-of-merits relative to the same devices containing ceramic transduction elements. An example of such a transducer is disclosed in U.S. Pat. No. 7,104,140 B2, incorporated by reference herein, which considers a trilaminar cantilever beam accelerometer that exploits the transverse extension, or 3-1 mode of the piezoelectric material. Here it is noted that the figure-of-merit for a piezoelectric transducer is defined by C. H. Sherman and J. L. Butler, Transducers and Arrays for Underwater Sound (Springer, New York, 2007), pp. 156-157, incorporated by reference herein, as Mo2/|Ze|, where Mo is the open-circuit voltage sensitivity and Ze is the electrical source impedance. Moreover, well below resonance where the transducer is in the stiffness-controlled region, the figure-of-merit can be expressed as Mo2CT when dielectric losses can be neglected and Mo2CT/tan δ when dielectric losses cannot be neglected. Here it is noted that CT and tan δ are the free capacitance and dielectric loss of the transducer. Generally speaking, the figure-of-merit can be further expressed in terms of the piezoelectric constants such that Mo2CT˜gijdij, where gij and dij are the piezoelectric voltage and charge constants, respectively. When a comparison of piezoelectric constants is made between ceramic and single crystal material the figure-of-merit upgrade provided by single crystal, in the absence of dielectric losses, ranges from approximately 6 to 12 dB. This can be gleaned by reviewing the material properties delineated for ceramic and single crystal in C. H. Sherman and J. L. Butler, Transducers and Arrays for Underwater Sound (Springer, New York, 2007), pp. 552-553, incorporated by reference herein. Nevertheless, the figure-of-merit upgrade essentially translates into how much lower the electronic noise floor will be relative to an identical device made from ceramic transduction elements. In this way the single crystal device can detect quieter sounds than its ceramic counterpart and can lead to improved sensing capabilities.
Now, in some applications involving piezoelectric accelerometers for low frequency fluidborne sound measurements, the figure-of-merit upgrade single crystals provides is not enough to meet the electronic noise floor requirement of a sensing system. This can be the case even when the transducer is coupled to a high-performance low noise preamplifier containing junction field effect transistors, such as that described by P. Horowitz and W. Hill, The Art of Electronics, (Cambridge University Press, New York, 1998), 2nd Ed., pp. 436-445, incorporated by reference herein. In these applications the sensitivity and/or capacitance of the accelerometer can be increased by the appropriate combination of additional sensing elements, and in doing so, the electronic noise floor can be reduced. For example, when higher sensitivity is required the sensing elements are electrically connected in series. Conversely, when higher capacitance is required the sensing elements are electrically connected in parallel. Moreover, series-parallel combinations can yield increases in both the sensitivity and capacitance.
Another method that can be used to increase the sensitivity is to position the fundamental resonance of the accelerometer as low as practically achievable. This approach is acceptable provided that the mechanical quality factor of the resonance is sufficiently low to preclude ringing, dynamic range limitations, mechanical cross-talk, and distorted directivity patterns. Here it is noted that the mechanical quality factor is inversely proportional to the resonance frequency and conforms to the well-known relation Qm=(ω0RmCm)−1 where ω0=(MmCm)−1/2 is the resonance frequency and Mm, Cm, and Rm are the mechanical mass, compliance, and damping, respectively. For a further discussion on the mechanical quality factor, see, e.g., C. H. Sherman and J. L. Butler, Transducers and Arrays for Underwater Sound (Springer, New York, 2007), pp. 81, 380-381, incorporated by reference herein. Moreover, the sensitivity of a piezoelectric accelerometer, well below resonance, is roughly proportional to the mechanical mass in the system or, Mo=k2Mm/N, which in turn is inversely proportional to the square of the resonance frequency. The variables k and N in the preceding equation are the electro-mechanical coupling coefficient and turns ratio. In this way, as the resonance frequency is lowered the mechanical mass increases which in turn raises the sensitivity. The theory behind this assertion is relatively well-known and is presented for the case of a flexural mode accelerometer in M. B. Moffett, D. H. Trivett, P. J. Klippel, and P. D. Baird, “A Piezoelectric, Flexural-Disk, Neutrally Buoyant, Underwater Accelerometer,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 45, No. 5, 1341-1346 (1998), incorporated by reference herein. Nevertheless, the consequence of lowering the resonance frequency is that the mechanical quality factor increases. Damping treatments or other suitable means are required to mitigate the adverse effects of such a dynamic system.
To further illustrate some of the points in the preceding paragraphs, the electronic noise floor of a piezoelectric hydrophone that is coupled to a voltage-mode preamplifier can be roughly estimated from the incoherent sum of the individual noise components according to Pn (En2+Et2+Ei2+Ej2)1/2/Mo, where En is the preamplifier noise voltage, Et is the thermal noise associated with the transducer, Ei is the preamplifier current noise flowing through the reactance associated with the transducer, and Ej is the Johnson noise associated with the input resistance of the preamplifier. The parameters can be defined further as Et=(4kBT tan δ/ωCT)1/2, Ei=InωCT, and Ej=(4kBTRi)1/2/ωRiCT, where kB is Boltzman's constant, T is the absolute temperature, and Ri is the input resistance of the preamplifier. It can be gleaned from the foregoing that the electronic noise floor, particularly at low frequencies can be minimized by maximizing the free capacitance CT and sensitivity Mo. Note that these formulae are valid for frequencies well below the resonance of the transducer and generally conform to the treatment given by T. B. Straw, “Noise Prediction for Hydrophone/Preamplifier Systems,” Naval Undersea Warfare Center Division Newport Report No. 10369, dated Jun. 3, 1993 (DTIC Report No. ADA265915), incorporated by reference herein. It is further noted that these equations are valid whether the hydrophone is sensitive to the acoustic pressure or the acoustic pressure-gradient, with the latter embodiment corresponding to the use of an accelerometer as the principal sensing component.
With regard to relaxor-based single crystal materials, binary and ternary formulations can be utilized for the transduction elements. Here it is noted that binary formulations can be comprised of, for example, lead magnesium niobate-lead titanate (PMN-PT) and lead zinc niobate-lead titanate (PZN-PT). Ternary formulations can be comprised of, for example, lead magnesium niobate-lead indium niobate-lead titanate (PMN-PIN-PT) and lead magnesium niobate-lead zirconate-lead titanate (PMN-PZ-PT). The motivation for developing ternary compounds was to improve the performance of the material with respect to temperature since it is relatively well known that the properties of single crystal materials can be compromised when they are subjected to moderate temperatures. For a discussion regarding the temperature characteristics associated with binary and ternary single crystal materials, see, for example, U.S. Pat. Publication No. 20090194732 A1 and C. H. Sherman and J. L. Butler, Transducers and Arrays for Underwater Sound (Springer, New York, 2007), pp. 552-553, each incorporated by reference herein.